While they are being accelerated to the operating rotation speed, turbocompressors and in particular axial turbocompressors have to pass through very unfavorable operating states. By way of example, turbocompressors in gas-turbine sets are operated with very low pressure ratios while being accelerated and with stepped-kinematic conditions that are very poor because of the low rotation speed. The front stages of an axial compressor therefore have to cope with poor incidence flow angles while, in contrast, the rear compressor stages are operated at the limit of their absorption capacity. Undesirable and poor flow instabilities therefore occur within the compressor. It is known from the prior art for mass-flow elements to be blown out during the compression process within a multi-stage axial compressor. It is also known, where these are provided, for rows of variable inlet guide vanes and rows of stator blades in the compressor to be moved, and in particular for a row of variable inlet guide vanes to be closed such that the mass flow being passed through is low. During operation, it is frequently found that the precautions taken do not make it possible to completely avoid the flow instabilities. The problem also occurs even when a turbocompressor is modified so as to carry a greater nominal mass flow. Hardware adaptations are then expensive and complex.